Knots and Links - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Knots and Links write by Dale Rolfsen. This book was released on 2003. Knots and Links available in PDF, EPUB and Kindle. Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book.""
Grid Homology for Knots and Links
Grid Homology for Knots and Links - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Grid Homology for Knots and Links write by Peter S. Ozsváth. This book was released on 2015-12-04. Grid Homology for Knots and Links available in PDF, EPUB and Kindle. Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.
Knots and Links
Knots and Links - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Knots and Links write by Peter R. Cromwell. This book was released on 2004-10-14. Knots and Links available in PDF, EPUB and Kindle. A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.
The Knot Book
The Knot Book - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Knot Book write by Colin Conrad Adams. This book was released on 2004. The Knot Book available in PDF, EPUB and Kindle. Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Knots, Links, Braids and 3-Manifolds
Knots, Links, Braids and 3-Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Knots, Links, Braids and 3-Manifolds write by Viktor Vasilʹevich Prasolov. This book was released on 1997. Knots, Links, Braids and 3-Manifolds available in PDF, EPUB and Kindle. This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.
